It is known that a light beam can be distorted as it passes through the atmosphere. In addition, other distortions are induced by the imperfections of receiving optical systems. Hence, adaptive optic systems have been devised to improve resolution of light waves by correcting these distortions.
Adaptive optic systems correct the distortions by measuring the shape of the wavefront distortion and reconstructing the wavefront. Adaptive optic systems generally accomplish this by sensing the wavefront with a wavefront sensor and thereafter, measuring the slope of the phase of detected light at several points along the wavefront by an array of light detectors. The resulting information is a matrix of measured phase differences between points on the wavefront. Phases of the various points forming the input wavefront are then calculated from the measured phase differences to reconstruct the wavefront.
For an ideal wavefront sensor, which measures phase differences with zero error, the wavefront phase can be calculated exactly by simply adding the phase differences between adjacent points. The relative phase between any two points, for such an ideal sensor, is independent of the path along which the phases are added. This is equivalent to stating that the vector curl of the phase differences (i.e. vector sum of the phase differences about a loop of points on the wavefront) is zero for a noiseless, ideal sensor.
In a real wavefront sensor there are always sources of error (noise), either due to the sensor, or due to the inherent quantum (photon) nature of light. In many practical applications the photon noise error is the primary limitation, and can be substantial. In such a system, the relative phases between two points depends on the path along which the phase differences are added. Thus, an accurate estimate of the wavefront can no longer be derived by simply adding the phase differences. The solution to this problem is to calculate a wavefront from the measured phase differences which is statistically optimum, or in other words, minimizes the effect of noise. This is equivalent to performing a least squares fit to the measured phase differences.
This least squares fit can be calculated exactly using standard numerical methods. The drawback to implementing an exact least squares fit is that the procedure is computationally intensive, and may require unacceptably large amounts of time or unacceptably complex and costly hardware. For example, a 10.times.10 element sensor array requires calculations involving a 100.times.100 element matrix. Likewise, a larger adaptive optic system utilizing a 100.times.100 element sensor array requires calculations involving a 10,000.times.10,000 element matrix, which is a time-consuming and costly process for even the largest of today's processors.
Accordingly, there has been an effort to develop systems which perform an approximate least squares wavefront fit to the measured phase differences. Many of these systems employ iterative schemes, as is the case for the invention presented herein. The criteria for judging these systems and their schemes are:
1. A low number of iterations required for acceptable convergence to the least squares solution. PA1 2. A low number of arithmetic operations required per iteration. PA1 3. Ease of implementation of the scheme.
Studies done to date indicate that the system presented herein meets all three criteria to an exceptional degree.